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Form 3 Applications of Percentages Practice

Form 3 · 40 practice questions with instant marking and worked solutions.

Applications of Percentages is an important part of the Form 3 mathematics curriculum. This topic develops percentages, conversions and percentage change. Begin by identifying what every number, symbol, diagram and unit represents. Translate the information into a mathematical relationship before calculating. Each line of working should have a purpose. Finally use estimation, substitution, an inverse operation, or a second representation to check the result. This habit separates a misunderstanding from a copying error and makes correction more useful.

A reliable approach to Applications of Percentages has four stages. First, mark the given information and the quantity required. Second, choose an appropriate representation, property or formula. Third, carry out the operations in a clear order while retaining signs and units. Fourth, return to the original context and decide whether the result is possible. For a graph or table, read the title, scale and labels before using a value. For algebra, inspect brackets, negative signs and the order of operations before simplifying.

The 40 original questions in this topic use a shared mathematical specification in Chinese and English. Difficulty rises from level 1 to level 5. Early questions establish the language and direct skills of Applications of Percentages; middle questions add two-step reasoning, conversions and common variations; later questions connect ideas and require a deliberate check. In multiple-choice work, calculate before looking at the choices. In fill-in and short-answer work, retain decisive steps. For true-or-false statements, support the decision with a calculation or counterexample.

Effective revision is more than recording a score. After completing the Applications of Percentages set, group errors by concept tags and decide whether each problem arose from interpretation, forming an expression, calculation, or presenting the answer. Retry the item on a later day without opening the solution, then test the same method with a different value. If the same tag appears repeatedly, return to the explanation and rebuild the concept. If signs or units are the issue, use a fixed pre-submission checklist.

Applications of Percentages should also connect with the rest of mathematics. Number and algebra supply calculation tools; measurement and geometry give spatial meaning; data handling asks what a result means. A learner who can explain aloud why every step is valid has moved beyond imitation. Estimate a reasonable range, complete an exact solution, and compare the two. Agreement between context, estimate and exact answer is strong evidence that the solution is sound.

This batch adds 20 questions, bringing the topic to 40. The new questions cover controlled variations of different concepts, with paired bilingual conditions, hints, worked solutions and reproducible checks.

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  1. 1 Basic
    In Applications of Percentages, calculate $80\times 20\%$. Choose the correct answer.
  2. 2 Basic
    In Applications of Percentages, calculate $120\times 25\%$. Give the numerical value only.

  3. 3 Basic
    In Applications of Percentages, calculate $120\times 50\%$. Show the essential working and give the numerical value.

  4. 4 Basic
    In Applications of Percentages, the value of $80\times 10\%$ is 9. Is this statement true?
  5. 5 Basic
    An item costs HK$512 after a 20% discount. Find the original price in dollars. Choose the correct answer.
  6. 6 Basic
    An item costs \$80 and sells for \$104. Find the percentage profit (as a percentage; a loss is negative). Give the answer only.

  7. 7 Basic
    An item's price rises by 20% and then falls by 10%. Find the overall percentage change (as a percentage; a decrease is negative). Show the essential working and give the answer.

  8. 8 Basic
    \$8000 is deposited at 10% p.a. compounded yearly. The amount after 3 years in dollars is 10400. Is this true?
  9. 9 Standard
    In Applications of Percentages, calculate $60\times 20\%$. Choose the correct answer.
  10. 10 Standard
    In Applications of Percentages, calculate $100\times 25\%$. Give the numerical value only.

  11. 11 Standard
    In Applications of Percentages, calculate $100\times 50\%$. Show the essential working and give the numerical value.

  12. 12 Standard
    In Applications of Percentages, the value of $60\times 10\%$ is 6. Is this statement true?
  13. 13 Standard
    A machine costs \$100000 and depreciates by 20% each year. Find its value after 2 years in dollars. Choose the correct answer.
  14. 14 Standard
    An item costs HK$720 after a 10% discount. Find the original price in dollars. Give the answer only.

  15. 15 Standard
    An item costs \$240 and sells for \$216. Find the percentage profit (as a percentage; a loss is negative). Show the essential working and give the answer.

  16. 16 Standard
    An item's price rises by 25% and then falls by 20%. The overall percentage change is 0. Is this true?
  17. 17 Advanced
    In Applications of Percentages, calculate $40\times 20\%$. Choose the correct answer.
  18. 18 Advanced
    In Applications of Percentages, calculate $80\times 25\%$. Give the numerical value only.

  19. 19 Advanced
    In Applications of Percentages, calculate $80\times 50\%$. Show the essential working and give the numerical value.

  20. 20 Advanced
    In Applications of Percentages, the value of $40\times 10\%$ is 5. Is this statement true?
  21. 21 Advanced
    \$10000 is deposited at 8% p.a. compounded yearly. Find the amount after 2 years in dollars. Choose the correct answer.
  22. 22 Advanced
    A machine costs \$100000 and depreciates by 25% each year. Find its value after 2 years in dollars. Give the answer only.

  23. 23 Advanced
    An item costs HK$350 after a 30% discount. Find the original price in dollars. Show the essential working and give the answer.

  24. 24 Advanced
    An item costs \$120 and sells for \$96. The percentage profit is 20. Is this true?
  25. 25 Challenging
    In Applications of Percentages, calculate $20\times 20\%$. Choose the correct answer.
  26. 26 Challenging
    In Applications of Percentages, calculate $60\times 25\%$. Give the numerical value only.

  27. 27 Challenging
    In Applications of Percentages, calculate $60\times 50\%$. Show the essential working and give the numerical value.

  28. 28 Challenging
    In Applications of Percentages, the value of $20\times 10\%$ is 2. Is this statement true?
  29. 29 Challenging
    An item's price rises by 30% and then falls by 20%. Find the overall percentage change (as a percentage; a decrease is negative). Choose the correct answer.
  30. 30 Challenging
    \$10000 is deposited at 20% p.a. compounded yearly. Find the amount after 2 years in dollars. Give the answer only.

  31. 31 Challenging
    A machine costs \$80000 and depreciates by 20% each year. Find its value after 2 years in dollars. Show the essential working and give the answer.

  32. 32 Challenging
    An item costs HK$448 after a 30% discount. The original price in dollars is 640. Is this true?
  33. 33 Elite
    In Applications of Percentages, calculate $160\times 20\%$. Choose the correct answer.
  34. 34 Elite
    In Applications of Percentages, calculate $40\times 25\%$. Give the numerical value only.

  35. 35 Elite
    In Applications of Percentages, calculate $40\times 50\%$. Show the essential working and give the numerical value.

  36. 36 Elite
    In Applications of Percentages, the value of $160\times 10\%$ is 17. Is this statement true?
  37. 37 Elite
    An item costs \$200 and sells for \$240. Find the percentage profit (as a percentage; a loss is negative). Choose the correct answer.
  38. 38 Elite
    An item's price rises by 10% and then falls by 10%. Find the overall percentage change (as a percentage; a decrease is negative). Give the answer only.

  39. 39 Elite
    \$2000 is deposited at 5% p.a. compounded yearly. Find the amount after 2 years in dollars. Show the essential working and give the answer.

  40. 40 Elite
    A machine costs \$80000 and depreciates by 10% each year. Its value after 3 years in dollars is 56000. Is this true?

The report lists what you got wrong and why. Only you can see it.

Common mistakes

Common mistakes in Applications of Percentages

This topic needs particular care with percentages, conversions and percentage change. The first mistake is applying a remembered rule before reading all conditions. The second is compressing working so much that a sign, bracket, decimal point or unit disappears. The third is accepting an impossible answer without checking: for example, a probability above one, a negative physical length, an angle outside the geometric constraints, or a result far from the estimate. Separate the conditions, model, calculation and check, and finish by stating what the answer represents.

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